[phyti39 (OP)]

Moving in time is a literal interpretation of the space and time merger proposed by Minkowski. It’s also another perspective of the moving light clock.
Light is emitted from a source in a direction p, perpendicular to x, the direction of motion, and reflects from a mirror a distance d=1, to a detector/counter. For the clock to function, the photon path must have an x and p component. The x component compensates for the motion of the clock at speed v. The p component becomes the active part of the clock. Since the photon speed is constant, its path in any direction generates a circular arc for the 90º between the p axis and x axis. This means the relative photon speed along p = c*sqrt(1-(v/c)^2) = c/γ, i.e. the clock ticks slower, the faster it moves past an observer.
With vt the x component and pt the p component, the relation can be rephrased as
1.   (vt)^2 + (pt)^2 = (ct)^2, or
2.   (light motion)^2 + (light motion)^2 = (light motion)^2, or
3.   (object motion)^2 + (object time)^2 = (object motion)^2
Conclusion:
Line 3 being so similar to line 2, allows a metaphorical interpretation as popularized by Briane Green and others. The clock moves in a 1-dimensional space, while/(simultaneously) the photon moves in a 2-dimensional space. The clock is counting spatial increments of (2γd) which are labeled in the traditional manner as ‘time’.
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[PmbPhy]

Moving in time is a literal interpretation of the space and time merger proposed by Minkowski.

That is incorrect. In fact its a common misconception in special relativity to think of it that way. I see that you've carried on this discussion in another forum too. This is a personal theory of yours and this forum is for "mainstream" physics, not personal theories. There is an entire sub forum for that at:
http://www.thenakedscientists.com/forum/index.php?board=18.0

It's called the New Theories sub forum.

The term "move" means that something has changed it's position in space from r₁ to r₂ during the time period t. Thus, saying that something is "moving in time" is quite meaningless.

It’s also another perspective of the moving light clock.
Light is emitted from a source in a direction p, ...

I'm confused. Please explain what p is. You later write "pt" as if pt is a distance yet you say that "p" is a direction. You'll have to be clearer as to what "p" is/means. You make it appear as if it's a speed. What is it the speed of? Is it the component of the speed of light in the vertical direction?

...perpendicular to x, the direction of motion, and reflects from a mirror a distance d=1, to a detector/counter. For the clock to function, the photon path must have an x and p component. The x component compensates for the motion of the clock at speed v. The p component becomes the active part of the clock. Since the photon speed is constant, its path in any direction generates a circular arc for the 90º between the p axis and x axis.

That is incorrect. You're speaking about the path that light takes in an inertial frame, presumably in a vacuum. As such the motion of light is independent of the source. The light doesn't follow an arc just because the source is moving. The correct derivation is at:
http://home.comcast.net/~peter.m.brown/sr/time_dilation.htm

Your argument is very problematic. You're all over the place and much is unclear. For example, you wrote Light is emitted from a source in a direction p.. While I'm sure you thought that you were being precise, that statement, combined with the diagram that you provided, really doesn't tell us where the light is emitted from and what the direction is. To draw a vector you need draw either the head and the tail, or a magnitude and direction. The magnitude can be represented by a line segment. The direction can be defined by placing an arrow head on one end of the line segment, oriented correctly.  See:
http://mathworld.wolfram.com/Vector.html

However what you did was to place a the letter p at the intersection of two lines. So your vector could be pointing from the origin of the coordinate system to the letter p or from the intersection of the two lines to the letter m. That also doesn't tell us where the source is located. You also have two curves. One is a blue straight line and the other is the quarter of a circle. T

Sorry but I can't make heads or tails out of your post. Please take another crack at it.

Please take a look at the derivation of the time dilation equation at my website. You'll see that it's the same as the one at:
http://simple.wikipedia.org/wiki/Light_clock

I hoped to write mine to be as clear as possible.

This means the relative photon speed along p = c*sqrt(1-(v/c)^2) = c/γ, i.e. the clock ticks slower, the faster it moves past an observer.

This is also incorrect and it's another reason why you can't discuss this in this forum and you'll have to move it to the New Theories sub forum. You have it that the speed of light is a function of v. The problem with that is that the speed if light has the same value in all inertial frames of motion.

Line 3 being so similar to line 2, allows a metaphorical interpretation as popularized by Briane Green and others. The clock moves in a 1-dimensional space, while/(simultaneously) the photon moves in a 2-dimensional space.

That also is incorrect. Both the clock and the photon are moving in a plane. Since it takes two numbers to specify a point in the space that they're moving in the space itself that they're in is 2-dimensional. That's the case even though the curve that light is moving on is a 1-d space. That's because each point on the curve is specified by two numbers. The 2 is the dimension of the space. What you did was to confuse the dimensionality of the curve with the dimensionality of the space that the curve is in. The curve is a subspace of the 2-d space in which all this takes place in.

[phyti39 (OP)]

PmbPhy;
I agree, the pt is confusing with the p axis. I'll change it.
This is not a personal theory, but a personal interpretation (as are all others presented in all forums, publications, etc) in terms of known physical phenomena, and not abstract theory. 

[yor_on]

should have seen this before commenting in the other thread.
Never thy mind, welcome Phyti.

[phyti39 (OP)]

PmbPhy

Thus, saying that something is "moving in time" is quite meaningless.

That is my point, since I do not agree with that popular sci-fi explanation. It's a distortion of the facts.
PmbPhy

This is also incorrect and it's another reason why you can't discuss this in this forum and you'll have to move it to the New Theories sub forum. You have it that the speed of light is a function of v. The problem with that is that the speed if light has the same value in all inertial frames of motion.

Only the p component of the light signal is a function of v. Since the observer is time dilated to the same extent as his clock, he measures .8 p units/.8 t units = 1 for light speed. Time dilation and length contraction complement each other to compensate for motion, resulting in x'/t' = x/t. This means all relations involving x and t produce the same results in all inertial frames.
The constant local (proper) time requires the altered perception of the observer, just as it alters the clock rate. The clock and observer are both material compositions. Td and lc make no distinctions.

It's easy to make revisions with a CAD system, but you have to remember to remove the old stuff, which I failed to do in this case. Here is the new and improved drawing and description.

Moving in time is a literal interpretation of the space and time merger proposed by Minkowski. It's also another perspective of the moving light clock. On the left, light is emitted from a source at the origin in a direction p, perpendicular to x, the direction of motion, and reflects from a mirror a distance d=1, to a detector/counter at the origin. For the clock to function, the photon path must have an x and p component. The x component compensates for the motion of the clock at speed v. The p component becomes the active part of the clock. Since the photon speed is constant, its path in any direction terminates on a circular arc for the 90º between the p axis and x axis. This means the relative photon speed along p is u = c*sqrt(1-(v/c)^2) = c/γ, i.e. the clock ticks slower, the faster it moves past an observer. 
With vt the x component and ut the p component, the relation can be rephrased as 
1.   (vt)^2 + (ut)^2 = (ct)^2, or
2.   (light motion)^2 + (light motion)^2 = (light motion)^2, or
3.   (object motion)^2 + (object time)^2 = (object motion)^2
Conclusion:
Line 3 being so similar to line 2, allows a metaphorical interpretation as popularized by Briane Green and others, by misinterpreting light motion as clock motion, when there is no clock motion in the p direction. The clock is counting spatial increments of (2γd) which are labeled in the traditional manner as "time".
On the right is the simultaneous perception of an observer moving with the clock.

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